Hello, everyone!
Here are the questions I'm concerned with. I'm an international student. Now I'm a freshman at Sofia University in Bulgaria. The department of mathematics and informatics is the best in the country (and not only) but it is hardly popular around the world. The entrance exams are really tough and the curriculum is very strong. You can compare it with the best mathematics departments in Russia. I have already decided that I want to do Phd in Math (particularly, some kind of geometry) in the USA and become a professor of Math in an American university. However, I was wondering if my bachelor degree will be strong enough to be accepted to a good math department in US. That's why I want you to see my future study plan- all the courses I plan to take. Imagine I have taken them all with exellent grades (I CAN do it). Will I be competitive enough in this way? I know that other factors as GRE, letters of recommendation, personal statement are also very important but at this time I'm wondering about my curriculum? Won't it be better to do a master degree first (probably in Utrecht Uni, the Netherlands) and then apply for PhD in the USA. Do you think that I will have even a little chance to be accepted to Harvard, MIT, Princeton or some other top-tier university? This year I started studying about GRE General so I think that in two years' time I'll have good scores not only in the quantitative part. I plan to take the GRE Math Subject during my junior year. I hope you give me some advice about what it'll be good to achieve in the next years in order to be accepted to a very good university in the USA.
I year:
Linear Algebra
Analytical Geometry
Differential & Integral Calculus I & II
Abstract Algebra I
Introduction to Programming
CS Practicum I
Subject of Geometry (topics: Erlangen Program of geometry; Geometry of Lobachevsky)
Selected Topics in Elementary Mathematics (topics: plane & solid geometry; combinatorial problems in the Number Theory)
II year:
Abstract Algebra II
Mathematical Analysis I & II
Differential Equations
Data Structures & Programming
CS Practicum II
Geometry & Topology
Introduction to Functional Analysis
Advanced Calculus I & II - workshop (based on problems given on mathematical competitions)
Differential Geometry
Numerical Analysis
Discrete Mathematics
Introduction to Number Theory
Introduction to Analytic Number Theory
III year:
Analytical Mechanics
Complex Analysis
Mathematical Logic
Partial Differential Equations
Lie Algebras & Groups
Geometrical Probabilities & Integral Geometry
Mathematical Programming
Introduction to Mechanics of Continua
Probability Theory I
Complex Analysis of Several Variables
Commutative Algebra
Functional Analysis - seminar
IV year:
Geometry of manifolds
Elements of Algebraic Geometry
Homological Algebra
Probability Theory II
Algebraic Topology & Differential Forms
General Topology
Hyperbolic Equations & Systems
Geometry & Mathematical Physics - seminar
Finite Geometries
Riemannian Geometry, Bochner Techniques & Vanishing Theorems
Theory of Groups
Descriptive Geometry
Preparation for the final state graduate exam
Thank you in advance!